FINITE-TYPE INTEGRABLE GEOMETRIC STRUCTURES

摘要

In this paper, we consider finite-type geometric structures of arbitrary order and solve the integrability problem for these structures. This problem is equivalent to the integrability problem for the corresponding G-structures. The latter problem is solved by constructing the structure functions for G-structures of order ≥1. These functions coincide with the well-known ones for the first-order G-structures, although their constructions are different. We prove that a finite-type G-structure is integrable if and only if the structure functions of the corresponding number of its first prolongations are equal to zero. Applications of this result to second- and third-order ordinary differential equations are noted.